Gamma Divergences

LEONARDO RIVEAUD; DIEGO M MATEOS; LAMBERTI PEDRO WALTER

Congreso; TREFEMAC 2021; 2021

Divergences have become a very useful tool for measuring similarity (or dissimilarity)between probability distributions. Depending on the field of application a more appropriatemeasure may be necessary. In this paper we introduce a family of divergences we call γ-divergences. They are based on the convexity property of the functions that generate them.We demonstrate that these divergences verify all the usually required properties, and weextend them to weighted probability distribution. We investigate their properties in thecontext of kernel theory. Finally, we apply our findings to the analysis of simulated andreal time series.